Carbon nanotube-based thermal interface materials and methods of making and using thereof

ABSTRACT

Multilayered or multitiered structures formed by stacking of vertically aligned carbon nanotube (CNT) arrays and methods of making and using thereof are described herein. Such multilayered or multitiered structures can be used as thermal interface materials (TIMs).

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of pending prior U.S. Ser. No.15/603,080 filed May 23, 2017, which claims priority to and benefit ofU.S. Ser. No. 62/343,458, filed May 31, 2016, which are herebyincorporated herein by reference in their entirety.

FIELD OF THE INVENTION

This invention is in the field of carbon nanotube arrays or sheets,particularly arrays or sheets which are stacked to form multilayered ormultitiered structures and methods of making and using thereof.

BACKGROUND OF THE INVENTION

Carbon nanotube (CNT) arrays are an attractive solution for enhancingthermal transport between surfaces. CNTs can be grown on metalsubstrates, eliminating concerns associated with pump out or voidingthat liquid thermal interface materials (TIMs) and greases may sufferfrom.

The high in-plane conductivity of individual nanotubes (as high as 3,000W/m-K) means that even at relatively low CNT densities (typical CNT fillfactors are on the order of 1%) the cross plane thermal conductance of aCNT-based TIM can be competitive with that of thermal grease.

Furthermore, the favorable deformation mechanics of CNTs allow them toefficiently conform to the asperities of adjoining surfaces, resultingin high contact areas at such interfaces between surfaces.

A key challenge, however, in CNT-based TIMs comes from the difficulty ingrowing very long CNTs on metal substrates. Unlike CNTs grown on siliconor other inert substrates, the catalyst required for CNT growth suffersfrom subsurface diffusion when grown on metal substrates, resulting inearly termination of tube growth. Furthermore, defects tend toaccumulate in CNTs as their height increases, resulting in CNT arrayswith conductivities significantly lower than the 3,000 W/m-K limitotherwise achievable with pristine tubes.

Thus, there is a need for overcoming the above mentioned difficulty ingrowing long CNT arrays on metal substrates and methods of makingmaterials which have good thermal transport properties.

Therefore, it is an object of the invention to provide CNT arrays orsheets and structures formed thereof and methods of making suchstructures having good thermal transport properties.

It is also an object of the invention to provide CNT arrays or sheetsand structures formed thereof which can provide high levels ofcompliance at the interface with one or more surfaces.

SUMMARY OF THE INVENTION

Multilayered or multitiered structures formed by stacking of verticallyaligned carbon nanotube (CNT) arrays and methods of making and usingthereof are described herein.

Two or more CNT arrays are typically stacked to form multilayered ormultitiered structures. Stacking of multiple CNT arrays, such that thenanostructure elements from opposing arrays form into tiers in the stackand become at least partially interdigitated with one another. Unlikethe stacking of a traditional material, stacked arrays of verticallyaligned nanostructures do no suffer from a linear (or worse) increase inthermal resistance with increasing thickness. Accordingly, the resultingmultilayered structures can mitigate the adverse impact of thickness andboundaries on energy transport as a result of the interdigitation of thenanostructure elements (i.e., CNTs) of the two or more arrays whencontacted. In contrast, for a typical material the resistance to heattransfer is directly proportional to the material's thickness, with anadditional interfacial resistance at the interfaces of a multilayeredstructure.

For multilayered or multitiered structures formed by stacking ofvertically aligned nanostructure materials of CNT arrays, wherein theCNTs of the arrays at least partially interdigitate within or into oneanother, effectively increasing the density of the CNTs. Typically, thedensity of CNTs grown on metal substrates is only about 1% of the totalvolume. When two adjacent layers of CNT arrays are stacked, for example,the density of heat conducting elements, such as CNTs or structuresformed thereof, is effectively doubled. As such the resistance to heattransfer per unit length is reduced in kind.

An advantage of the multilayered or multitiered structures formed bystacking of two or more CNT arrays over traditional bulk materials comesat the interface of the arrays. For example, resistance to heat transferincreases not only due to the increase in thickness of a multilayerstack, but also due to the interfacial resistances between the tiers.Accordingly, between any two adjacent tiers, the boundary between thetwo tiers is the location of poor heat transfer, relative to the bulkmaterial due to poor contact between the tiers, as well as due toscattering of energy carriers (e.g. electrons or phonons) at theboundary. When interdigitated, the high aspect ratio of thenanostructures, such as CNTs, results in a very high contact areabetween the tiers minimizing the poor contact area contribution to theinter tier interfacial resistance. Although Kapitza (scattering)resistance cannot be completely eliminated the resistance can be reducedby applying, infiltrating, or backfilling the array or sheet with apolymer, wax, or other secondary material that facilitatesthermal/energy transport across the boundary. This transportfacilitation may be through the formation of a covalent or weak atomicinteraction between the CNT and a secondary material, reduction ofacoustic phononic transport mismatch relative to air, or other types ofmechanisms.

In one embodiment, nanostructure elements which form the array arevertically aligned carbon nanotubes (CNTs). In some embodiments, the CNTarray is grown on a metal substrate which is formed of aluminum, copperor steel or comprises aluminum, copper or steel, or alloys thereof. Inanother embodiment, the CNT array is formed on a flexible, electricallyand thermally conductive substrate, such as graphite. In yet anotherembodiment, the CNT array is grown on an electrically insulatingsubstrate, such as a flexible ceramic. In one embodiment, the inertsupport for the CNT array is a piece of metal foil, such as aluminumfoil. In some instances only one surface (i.e., side) of the metal foilcontains an array of vertically aligned CNTs anchored to the surface orthe substrate/support. In other cases, both surfaces (i.e., sides) ofthe substrate/support, such as a metal foil, contain a coated array ofaligned CNTs anchored to the surface. As another example, CNT sheets canbe coated on one or both sides and do not require an inert support.

In embodiments described herein two or more CNT arrays are stacked atopone another and the nanostructure elements of the individual arrays,such as the CNTs or some portion thereof, fully or substantiallyinterdigitate within one another; “substantially,” as used herein,refers to at least 95%, 96%, 97%, 98%, or 99% interdigitation betweenthe nanostructure elements (i.e., CNTs) of the individual arrays. Insome embodiments, the extent of interdigitation is in the range of about0.1% to 99% or at least about 1%, 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%,80%, 90%, or 95%. In certain other embodiments, the two CNT arrays maybe interdigitated only at the tips of the nanostructure elements (i.e.,CNTs) of the individual arrays. By stacking two or more individual CNTarrays, wherein the nanostructure elements of the individual arraysinterdigitate when stacked adjacently, it is possible to formmultilayered or multitiered structures.

In certain embodiments, one or more individual nanostructure elements,such as CNTs, of the array may navigate through another when adjacentCNT arrays are brought in contact during the stacking process.

In some embodiments, the individual nanostructure elements, such asCNTs, of the array may interdigitate and form into larger structures,such as superstructures, such as, but not limited to, tube bundles,clumps, or rows. Such superstructures may be formed through mechanismssuch as capillary clumping or when a polymer coating has been applied tothe CNT arrays prior to, during, or following the stacking process.

In certain embodiments, adjacent tiers formed by stacking of CNT arraysare formed via simple dry contact, using entanglement, friction or weakattraction forces between the nanostructures present therein to keep theresulting interdigitated structure together. In certain otherembodiments the stacked structure resulting therefrom may optionally beinfiltrated or backfilled with a polymer, wax, liquid metal, or othersuitable material that solidifies inside the stacked structure in orderto hold the interdigitated arrays together.

In some embodiments the polymer, wax, liquid metal, or other suitablematerial can reduce the transport resistance between the multiple layersor tiers formed, resulting from improved contact area, a reduction inscattering, or other related mechanisms. In yet other embodiment thetiers formed by stacking of arrays may be bonded by use of an adhesiveor a phase-change material.

CNT arrays and the multilayered or multitiered structures formed bystacking of such CNT arrays exhibit both high thermal conductance andmechanical durability. The multilayered or multitiered structures formedby stacking of CNT arrays described herein can be used as thermalinterface materials (TIMs). Accordingly, such materials are well suitedfor applications where repeated cycling is required. For example, theycan be employed as thermal interface materials during ‘burn-in’ testingof electrical components, such as chips. In some embodiments, the inertsupport/substrate is a surface of a conventional metal heat sink orspreader. This functionalized heat sink or spreader may then be abuttedor adhered to a heat source, such as an integrated circuit package. SuchTIM materials can also be placed or affixed in between a heat source anda heat sink or heat spreader, such as between an integrated circuitpackage and a finned heat exchanger, to improve the transfer of heatfrom the heat source to the heat sink or spreader.

The CNT arrays and the multilayered or multitiered structures formed bystacking of such CNT arrays described herein can be used as thermalinterface materials (TIMs) in personal computers, server computers,memory modules, graphics chips, radar and radio-frequency (RF) devices,disc drives, displays, including light-emitting diode (LED) displays,lighting systems, automotive control units, power-electronics, solarcells, batteries, communications equipment, such as cellular phones,thermoelectric generators, and imaging equipment, including MRIs.

In certain embodiments, the multilayered or multitiered structuresformed by stacking of CNT arrays are useful as TIMs in low contactpressure and/or low ambient pressure applications, such as in aerospaceapplications where such TIMs could be used in satellites or spacevehicles/systems. In certain embodiments, the multilayered ormultitiered structures formed by stacking of CNT arrays are useful attemperatures below ambient, below freezing, or at cryogenic temperatures(such as experienced in space).

The CNT arrays and the multilayered or multitiered structures formed bystacking of such CNT arrays described herein can also be used forapplications other than heat transfer. Examples include, but are notlimited to, microelectronics, through-wafer vertical interconnectassemblies, and electrodes for batteries and capacitors. Currently,copper and aluminum foil are used as the backing materials for the anodeand cathode in lithium ion batteries.

The multilayered or multitiered structures formed by stacking of suchCNT arrays could also be used for electromagnetic shielding.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B are non-limiting schematics of amultilayered/multitiered structure formed by stacking of carbon nanotube(CNT) arrays. FIG. 1A shows a schematic of a thermal interface material(TIM) having a single tier, 100, with arrays of carbon nanotubes, 110,on each side of the substrate and wherein the TIM is placed between anelectronic device, 200, and a heat sink, 300. FIG. 1B shows a schematicof a thermal interface material (TIM) having three tiers, 100, where thethree-tiered TIM is placed between an electronic device, 200, and a heatsink, 300.

FIG. 2 is a graph showing the heat transfer coefficient for dry stacksof three TIMs on aluminum (Al) substrates over two test cycles.

FIG. 3 is a graph showing the heat transfer coefficient for wax-bondedstacks of three TIMs on aluminum (Al) substrates over two test cycles.

FIG. 4 is a bar graph showing the compressibility of one-, two-, andfour-tiered CNT-based TIMs and of several commercially available TIMs.Normalized compression was measured at 100 psi.

FIG. 5 is a bar graph showing the rebound after compression of one-,two-, and four-tiered CNT-based TIMs and of several commerciallyavailable TIMs. TIM normalized rebound was measured at 7 psi followingcompression to 100 psi.

FIG. 6 is a graph showing the effective thermal conductivity ofone-tiered and stacked two- and four-tiered TIMs.

FIG. 7 is a graph showing compliance and compression sets for aCNT-based TIM tested at successive pressures of 30 psi, 50 psi, 60 psi,and 80 psi at a temperature of 80° C.

FIG. 8 is a graph showing the effect of increased contact pressure(x-axis) on thermal resistance (y-axis) on a CNT-based stacked TIM.

FIG. 9 is a graph showing the change in thermal resistance over time(x-axis) of a CNT-based stacked TIM over greater than 5,000 insertionsat a pressure of 80 psi.

FIG. 10 is a graph showing thermal resistance hysteresis of a CNT-basedstacked TIM, upon initial install and post re-work, at pressures of 0 to500 psi.

FIG. 11 is a graph of the thermal resistance as a function of junctiontemperature of a single-tiered CNT-based TIM, a three-tiered CNT-basedTIM, a CNT-based TIM wherein a gap pad is sandwiched between two tiersof CNT-based TIM, and an indium benchmarking sample.

FIG. 12 is a graph showing the normalized thickness of several TIMmaterials as a function of pressure.

DETAILED DESCRIPTION OF THE INVENTION I. Definitions

“Thermal Interface Material” (TIM), as used herein, refers to a materialor combination of materials that provide high thermal conductance andmechanical compliance between a heat source and heat sink or spreader toeffectively conduct heat away from a heat source.

“Compliant” or “Compliance,” as used herein, refers to the ability of amaterial to conform when contacted to one or more surfaces such thatefficient conformance to the asperities of the adjoining surface resultsin sufficient or high contact areas at the interfaces between thesurfaces and the material.

“Interdigitation” or “Interdigitating”, as used herein, refers to theability and or degree which one or more individual nanostructureelements of an array or sheet to infiltrate or penetrate into theadjacent nanostructure elements of another array or sheet when the twodifferent arrays or sheets are contacted or stacked.

“Carbon Nanotube Array” or “CNT array” or “CNT forest”, as used herein,refers to a plurality of carbon nanotubes which are vertically alignedon a surface of a material. Carbon nanotubes are said to be “verticallyaligned” when they are substantially perpendicular to the surface onwhich they are supported or attached. Nanotubes are said to besubstantially perpendicular when they are oriented on average within 30,25, 20, 15, 10, or 5 degrees of the surface normal.

“Carbon Nanotube Sheet” or “CNT sheet”, as used herein, refers to aplurality of carbon nanotubes which are aligned in plane to create afree-standing sheet. Carbon nanotubes are said to be “aligned in plane”when they are substantially parallel to the surface of the sheet thatthey form. Nanotubes are said to be substantially parallel when they areoriented on average greater than 40, 50, 60, 70, 80, or 85 degrees fromsheet surface normal.

“Coating material” as used herein, generally refers to polymers and/ormolecules that can bond to CNTs through van der Waals bonds, π-πstacking, mechanical wrapping and/or covalent bonds and bond to metal,metal oxide, or semiconductor material surfaces through van der Waalsbonds, π-π stacking, and/or covalent bonds.

“Elastic recovery” as used herein, refers to the ability of a materialto return to its original shape following compression, expansion,stretching, or other deformation.

“Compression set” as used herein, refers to the permanent deformation ofa material which remains when a force, such as compression, was appliedto the material and the force was subsequently removed.

Numerical ranges disclosed in the present application include, but arenot limited to, ranges of temperatures, ranges of pressures, ranges ofmolecular weights, ranges of integers, ranges of conductance andresistance values, ranges of times, and ranges of thicknesses. Thedisclosed ranges of any type, disclose individually each possible numberthat such a range could reasonably encompass, as well as any sub-rangesand combinations of sub-ranges encompassed therein. For example,disclosure of a pressure range is intended to disclose individuallyevery possible temperature value that such a range could encompass,consistent with the disclosure herein.

II. Coated Carbon Nanotube Arrays or Sheets

A. Carbon Nanotube Arrays

Carbon nanotube arrays are described herein contain a plurality ofcarbon nanotubes supported on, or attached to, the surface of an inertsubstrate/support, such as a metallic (e.g., Al or Au) foil, metalalloys (i.e., steel). In some embodiments, the substrate/support can bea flexible, electrically, and thermally conductive substrate, such asgraphite or other carbon-based material. In yet other embodiments, thesubstrate/support can be an electrically insulating substrate such as aflexible ceramic. The CNT arrays can be formed using the methodsdescribed below. The CNTs are vertically aligned on thesubstrate/support. CNTs are said to be “vertically aligned” when theyare substantially perpendicular to the surface on which they aresupported or attached. Nanotubes are said to be substantiallyperpendicular when they are oriented on average within 30, 25, 20, 15,10, or 5 degrees of the surface normal.

Generally, the nanotubes are present at a sufficient density such thatthe nanotubes are self-supporting and adopt a substantiallyperpendicular orientation to the surface of the multilayer substrate.Preferably, the nanotubes are spaced at optimal distances from oneanother and are of uniform height to minimize thermal transfer losses,thereby maximizing their collective thermal diffusivity.

The CNT arrays contain nanotubes which are continuous from the top ofthe array (i.e., the surface formed by the distal end of the carbonnanotubes when vertically aligned on the multilayer substrate) to bottomof the array (i.e., the surface of the multilayer substrate). The arraymay be formed from multi-wall carbon nanotubes (MWNTs), which generallyrefers to nanotubes having between approximately 4 and approximately 10walls. The array may also be formed from few-wall nanotubes (FWNTs),which generally refer to nanotubes containing approximately 1-3 walls.FWNTs include single-wall carbon nanotubes (SWNTs), double-wall carbonnanotubes (DWNTS), and triple-wall carbon nanotubes (TWNTs). In certainembodiments, the nanotubes are MWNTs. In some embodiments, the diameterof MWNTs in the arrays ranges from 10 to 40 nm, more preferably 15 to 30nm, most preferably about 20 nm. The length of CNTs in the arrays canrange from 1 to 5,000 micrometers, preferably 5 to 5000 micrometers,preferably 5 to 2500 micrometers, more preferably 5 to 2000 micrometers,more preferably 5 to 1000 micrometers. In some embodiments, the lengthof CNTs in the arrays can range from 1-500 micrometers, even morepreferably 1-100 micrometers.

The CNTs display strong adhesion to the multilayer substrate. In certainembodiments, the CNT array or sheet will remain substantially intactafter being immersed in a solvent, such as ethanol, and sonicated for aperiod of at least five minutes. In particular embodiments, at leastabout 90%, 95%, 96%, 97%, 98%, 99%, or 99.9% of the CNTs remain on thesurface after sonication in ethanol.

B. Carbon Nanotube Sheets

Carbon nanotube sheets are also described herein. The sheets contain aplurality of carbon nanotubes that support each other through strong vander Waals force interactions and mechanical entanglement to form afreestanding material. The CNT sheets can be formed using the methodsdescribed below. The CNTs form a freestanding sheet and are aligned inplane with the surface of this sheet. CNTs are said to be “aligned inplane” when they are substantially parallel to the surface of the sheetthat they form. Nanotubes are said to be substantially parallel whenthey are oriented on average greater than 40, 50, 60, 70, 80, or 85degrees from sheet surface normal.

Generally, the nanotubes are present at a sufficient density such thatthe nanotubes are self-supporting and adopt a substantially parallelorientation to the surface of the sheet. Preferably, the nanotubes arespaced at optimal distances from one another and are of uniform lengthto minimize thermal transfer losses, thereby maximizing their collectivethermal diffusivity.

The CNT sheets may be formed from multi-wall carbon nanotubes (MWNTs),which generally refers to nanotubes having between approximately 4 andapproximately 10 walls. The sheets may also be formed from few-wallnanotubes (FWNTs), which generally refers to nanotubes containingapproximately 1-3 walls. FWNTs include single-wall carbon nanotubes(SWNTs), double-wall carbon nanotubes (DWNTS), and triple-wall carbonnanotubes (TWNTs). In certain embodiments, the nanotubes are MWNTs. Insome embodiments, the diameter of MWNTs in the arrays ranges from 10 to40 nm, more preferably 15 to 30 nm, most preferably about 20 nm. Thelength of CNTs in the sheets can range from 1 to 5,000 micrometers,preferably 100 to 5000 micrometers, preferably 500 to 5000 micrometers,more preferably 1000 to 5000 micrometers. In some embodiments, thelength of CNTs in the sheets can range from 1-500 micrometers, even morepreferably 1-100 micrometers.

C. Coating(s)/Coating Materials

The CNT array or sheet can include a coating or coating material (termscan be used interchangeably) which adheres or is bonded to the CNTs. Thecoating/coating material can be applied as described below. In someembodiments, the coating contains one or more oligomeric materials,polymeric materials, waxes, or combinations thereof. In otherembodiments, the coating contains one or more non-polymeric materials.In some embodiments, the coating can contain a mixture of oligomeric,waxes, and/or polymeric material and non-polymeric materials.

In certain embodiments, the coating material(s) act as a bondingagent(s) which can bonded, such as chemically, the carbon nanotubes ofthe stacked arrays or sheets. Without limitation, such coatingmaterial(s) which can act as bonding agents(s) can be selected fromadhesives (i.e., acrylate adhesives) and a phase change material (i.e.,a wax or waxes).

In some embodiments, the coating which adheres or is bonded to the CNTsof an array is applied before two or more CNT arrays or sheets arestacked while in other embodiments, the coating which adheres or isbonded to the CNTs of an array is applied following stacking of two ormore CNT arrays or sheets. In yet other embodiments, the coating isinfiltrated or backfilled into multilayered or multitiered structuresformed of stacked CNT arrays or sheets and adheres or is bonded to theCNTs of the arrays forming the structure. As used herein, “infiltration”or “infiltrated” refer to a coating material(s) which are permeatedthrough at least some of the carbon nanotubes of the arrays or sheetswhich were stacked to form the multilayered or multitiered structures.In some embodiments, the extent of infiltration is in the range of0.1-99.9%. In some embodiments, the infiltrated coating material atleast partially fills the interstitial space between carbon nanotubeswhile in some other embodiments the infiltrated coating coats at leastsome of the surfaces of the carbon nanotubes, or both. In someembodiments, the infiltrated coating material fills the all orsubstantially all (i.e., at least about 95%, 96%, 97%, 98%, or 99%) ofthe interstitial space between carbon nanotubes present in the tiers orlayers of the structure formed by stacking of the CNT arrays or sheets.

A variety of materials can be coated onto the CNT arrays or sheets,prior to stacking, during stacking, or following stacking. In particularembodiments, the coatings can cause a decrease in the thermal resistanceof the CNTs of arrays or sheets of structure having a plurality oflayers or tiers, as defined herein. The coatings can be appliedconformally to coat the tips and/or sidewalls of the CNTs. It is alsodesirable that the coating be reflowable as the interface is assembledusing, for example, solvent, heat or some other easy to apply source.Polymers used as coatings must be thermally stable up to at least 130°C. In some embodiments, the coating is readily removable, such as byheat or dissolution in a solvent, to allow for “reworking” of theinterface. “Reworking”, as used herein, refers to breaking the interface(i.e., removing the coating) by applying solvent or heat.

1. Polymeric Coating Materials

In some embodiments, the coating is, or contains, one or more polymericmaterials. The polymer coating can contain a conjugated polymer, such asan aromatic, heteroaromatic, or non-aromatic polymer, or anon-conjugated polymer.

Suitable classes of conjugated polymers include polyaromatic andpolyheteroaromatics including, but not limited to, polythiophenes(including alkyl-substituted polythiophenes), polystyrenes,polypyrroles, polyacetylenes, polyanilines, polyfluorenes,polyphenylenes, polypyrenes, polyazulenes, polynaphthalenes,polycarbazoles, polyindoles, polyazepines,poly(3,4-ethylenedioxythiophenes), poly(p-phenyl sulfides), andpoly(p-phenylene vinylene). Suitable non-aromatic, conjugated polymersinclude, but are not limited to, polyacetylenes and polydiacetylenes.The polymer classes listed above include substituted polymers, whereinthe polymer backbone is substituted with one or more functional groups,such as alkyl groups. In some embodiments, the polymer is polystyrene(PS). In other embodiments, the polymer is poly(3-hexythiophene) (P3HT).In other embodiments, the polymer is poly(3,4-3thylenedioxythiophene)(PEDOT) or poly(3,4-3thylenedioxythiophene) poly(styrenesulfonate)(PEDOT:PSS).

In other embodiments, the polymer is a non-conjugated polymer. Suitablenon-conjugated include, but are not limited to, polyvinyl alcohols(PVA), poly(methyl methacrylates) (PMMA), polydimethylsiloxanes (PDMS),polyurethane, silicones, acrylics, and combinations (blends) thereof.

In other embodiments, the polymer is a paraffin wax. In otherembodiments, the polymer is a synthetic wax such as Fischer-Tropschwaxes or polyethylene waxes. In other embodiments, the polymer is a waxthat has a melting temperature above 80, 90, 100, 110, or 120° C.,preferably above 130° C.

In other embodiments, the polymer is an adhesive, such as, but notlimited to, a hot glue or hot melt adhesive that combines wax,tackifiers and a polymer base to provide improved adhesion properties toone or more surfaces. In some embodiments, the adhesive is a pressuresensitive adhesive. In certain other embodiments, the adhesive is amonomer that polymerizes upon contact with air or water such as acyanoacrylate. In yet other embodiments, the adhesive is a combinationof a pressure sensitive adhesive and a thermally activated (oractivatable) adhesive polymers which enhances ease of adhesion of amultilayered or multitiered structure described herein which includessuch a combination of coatings to a surface(s), by way of the pressuresensitive adhesive and additional and more permanent or semi-permanentadhesion by way of the thermal adhesive.

D. Other Coating Materials

1. Metallic Nanoparticles

The CNT arrays or sheets can additionally be coated with one or moremetal nanoparticles. One or more metal nanoparticles may be adsorbed tothe distal ends and/or sidewalls of the CNTs to bond the distal endsand/or sidewalls of the CNTs to a surface, reduce thermal resistancebetween the CNT array or sheet and a surface, or combinations thereof.Metal nanoparticles can be applied to CNT arrays or sheets using avariety of methods known in the art.

Examples of suitable metal nanoparticles include palladium, gold,silver, titanium, iron, nickel, copper, and combinations thereof.

2. Flowable or Phase Change Materials

In certain embodiments, flowable or phase change materials are appliedto the CNT arrays or sheets prior to stacking, during stacking, orfollowing stacking. Flowable or phase change materials may be added tothe CNT array or sheet to displace the air between CNTs and improvecontact between the distal ends and/or sidewalls of CNTs and a surface,and as a result reduce thermal resistance of the array or sheet and thecontact between the array or sheet and a surface, or combinationsthereof. Flowable or phase change materials can be applied to CNT arraysusing a variety of methods known in the art.

Examples of suitable flowable or phase change materials include paraffinwaxes, polyethylene waxes, hydrocarbon-based waxes in general, andblends thereof. Other examples of suitable flowable or phase changematerials that are neither wax nor polymeric include liquid metals,oils, organic-inorganic and inorganic-inorganic eutectics, and blendsthereof. In some embodiments, the coating material, such as anon-polymeric coating material and the flowable or phase change materialare the same material or materials.

III. Multilayered or Multitiered Structures

The CNT arrays or sheets described above can be stacked according to themethods described below to afford multilayered or multitieredstructures. A non-limiting example of a three layered/tiered structureis shown in the schematic of FIG. 2 (right side). A layer or tier isformed by contacting/stacking the carbon nanotubes of two CNT arrays orsheets, which interdigitate at least partially, and which may optionallybe coated with a suitable coating material as described herein.

In some embodiments the multilayered or multitiered structures canfurther include a coating, a coating of metallic nanoparticles, and/or acoating of flowable or phase change materials on the nanostructureelements, such as CNTs, of the arrays.

At least two CNT arrays or sheets can be stacked to form themultilayered or multitiered structures. For example, FIG. 2 showsstacking of three CNT arrays (right side). By using more CNT arrays thethickness of the multilayered or multitiered structures can be increasedas needed. In some embodiments, up to 5, 10, 15, 20, 25, 30, or more CNTarrays or sheets can be stacked according to the method described above.The thickness of the resulting multilayered or multitiered structuresformed by stacking can be in the range 1-10,000 microns or more. In someembodiments, the thickness of the resulting multilayered or multitieredstructures formed by stacking can be 1-3,000 micrometers, even morepreferably 70-3,000 micrometers. In some embodiments, the number oflayers and/or thickness is based on the thickness of the CNT forestformed on the arrays used in the stacking process.

In a non-limiting embodiment, at least two vertically aligned arrays orsheets formed on supports/substrates are stacked/contacted such that thenanostructure elements, such as CNTs, of the arrays at least partiallyinterdigitate on contact. In one embodiment full interdigitation ofnanostructure elements of the arrays occurs within one another whenstacked. In other embodiments the arrays may interdigitate only at thetips of the nanostructure elements, such as CNTs. In yet otherembodiments, the individual nanostructures can navigate through thenanostructures of the adjacent array during the interdigitating processand the nanostructure elements of the individual arrays, such as theCNTs or some portion thereof, fully or substantially interdigitatewithin one another; “substantially,” as used herein, refers to at least95%, 96%, 97%, 98%, or 99% interdigitation between the nanostructureelements of the individual arrays. In some embodiments, the extent ofinterdigitation is in the range of about 0.1% to 99% or at least about1%, 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, or 95%.

In some embodiments the nanostructures of the stacked arrays, whichinterdigitate at least partially, may also form into largersuperstructures, such as, but not limited to, tube bundles, clumps, orrows. These superstructures may be formed through mechanisms such ascapillary clumping or by way of application of a polymer coating priorto, during, or following the stacking process.

In some embodiments, a polymer coating and/or adhesive, or other coatingas described above, is applied to the CNT array(s) which aresubsequently stacked. In such embodiments, the thickness of the coatingand/or adhesive, or other coating as described above, is about 1-1000nm, more preferable 1-500 nm, and most preferably 1-100 nm.

In addition to the above, the favorable deformation mechanics of CNTspresent in the multilayered or multitiered structures allow them toefficiently conform to the asperities of adjoining surfaces, resultingin high contact areas at the interfaces.

A. Reduction in Thermal Resistance

The CNT arrays or sheets and the multilayered or multitiered structuresformed by stacking of such CNT arrays described herein exhibit reducedthermal resistance. The thermal resistance can be measured using avariety of techniques known in the art, such as the photoacoustic (PA)method.

In one embodiment, the thermal resistance of the CNT arrays or sheetsand the multilayered or multitiered structures formed by stacking ofsuch CNT arrays or sheets is reduced by at least about 25%, 30%, 35%,40%, 45%, 50%, 55%, 60%, 65%, 70% or greater compared to single tieredstructures when measured, for example, using the photoacoustic method.In certain embodiments, the CNT arrays or sheets and the multilayered ormultitiered structures formed by stacking of such CNT arrays or sheetsexhibit thermal resistances of less than about 1.0, 0.9, 0.8, 0.7, 0.6,0.5, 0.4, 0.3, 0.2, or 0.1 cm² K/W. In such embodiments, the thermalresistance is about 0.4, preferably about 0.3 cm² K/W. In certainembodiments, the CNT arrays or sheets and the multilayered ormultitiered structures formed by stacking of such CNT arrays or sheetsexhibit thermal resistances of between about 1 and 0.1 cm² K/W. In suchembodiments, the thermal resistance is about 1, 0.9, 0.8, 0.7, 0.6, 0.5,0.4, 0.3, 0.2, or 0.1 cm² K/W. In some embodiments, the thermalresistance value of a multilayered or multitiered structures formed bystacking of CNT arrays or sheets is the same or substantially unchangedas compared to the value(s) of the single layer arrays used to form thestack; “substantially,” as used herein refers to less than a 10%, 5%,4%, 3%, 2%, or 1% change.

In some instances, the multilayered or multitiered structures formed bystacking of CNT arrays or sheets, when used, for example, as thermalinterface materials (TIMs) exhibit thermal resistance hysteresis andstable operation over a wide pressure range of 0 to 500 psi, 0 to 400psi, 0 to 300 psi, 0 to 200 psi, or 0 to 100 psi, when increasing anddecreasing the pressure on the TIM in the aforementioned ranges.

In one embodiment, the apparent thermal conductivity of the CNT arraysor sheets and the multilayered or multitiered structures formed bystacking of such CNT arrays or sheets is increased by at least about25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 65%, 70% or greater compared tosingle tiered structures. In some embodiments, the CNT arrays or sheetsand the multilayered or multitiered structures formed by stacking ofsuch CNT arrays or sheets exhibit conductance values in the range ofabout 1-2500 W/m-K, 1-2000 W/m-K, 1-1500 W/m-K, 1-1000 W/m-K, 1-500W/m-K, 5-500 W/m-K, 5-400 W/m-K, 5-300 W/m-K, 5-200 W/m-K, 5-150 W/m-K,5-100 W/m·K, or 3-30 W/m-K.

A coating may be optionally applied to the CNT arrays or sheets priorto, during, or following stacking to form multilayered or multitieredstructures formed by stacking of such CNT arrays or sheets. Coating(s)were shown to be an effective means for increasing the contact area andreducing the thermal resistance of CNT forest thermal interfaces. Thebonding process added by inclusion of nanoscale coatings aroundindividual CNT contacts includes, for example, pulling, throughcapillary action, of additional CNTs close to the interface to increasecontact area.

The multilayered or multitiered structures, demonstrate good compliance,i.e., the ability to conform when contacted to one or more surfaces ofmaterial(s) (such as a die or chip). Compliant multilayered ormultitiered TIMs have contact areas at interfaces between surface(s) ofmaterial(s) and the TIM, such that the compliance of the multilayered ormultitiered TIMs, expressed as a percentage value, is between about 1%to 50%, 1% to 40%, 1% to 30%, 1% to 25%, 1% to 20%, or 1% to 10% of thetotal thickness of the TIM.

The multilayered or multitiered structures also demonstrate excellentelastic recovery properties following one or more repeated deformations,typically compressions, at varying pressures up to about 50, 100, 200,300, 400, 500 psi, or greater (see Example data). Elastic recovery ofthe multilayered or multitiered structures, expressed as a percentagevalue, following one or more compressions can be greater than about 50%,60%, 70%, 80%, 90%, 91%, 92%, 93%, 94%, 95%, 96%, 97%, 98%, or 99%. Insome instances, the multilayered or multitiered structures describedalso demonstrate compression set properties following one or morerepeated deformations, typically compressions, at varying pressures upto about 50, 100, 200, 300, 400, 500 psi, or greater. Compression set ofthe multilayered or multitiered structures, expressed as a percentagevalue, following one or more compressions can be less than about 20%,15%, 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1%, 0.9%, 0.8%, 0.7%, 0.6%,0.5%, 0.4%, 0.3%, 0.2%, or 0.1%.

IV. Methods for Preparing Multilayered or Multitiered Structures

A. Carbon Nanotube Arrays

Carbon nanotube arrays can be prepared using techniques well known inthe art. In one embodiment, the arrays are prepared as described in U.S.Publication No. 2014-0015158-A1, incorporated herein by reference. Thismethod involves the use of multilayer substrates to promote the growthof dense vertically aligned CNT arrays and provide excellent adhesionbetween the CNTs and metal surfaces.

The multilayer substrates contain three or more layers deposited on aninert support, such as a metal surface. Generally, the multilayersubstrate contains an adhesion layer, an interface layer, and acatalytic layer, deposited on the surface of an inert support.Generally, the support is formed at least in part from a metal, such asaluminum, platinum, gold, nickel, iron, tin, lead, silver, titanium,indium, copper, or combinations thereof. In certain instances, thesupport is a metallic foil, such as aluminum or copper foil. The supportmay also be a surface of a device, such as a conventional heat sink orheat spreader used in heat exchange applications.

The adhesion layer is formed of a material that improves the adhesion ofthe interface layer to the support. In certain embodiments, the adhesionlayer is a thin film of iron. Generally, the adhesion layer must bethick enough to remain a continuous film at the elevated temperaturesused to form CNTs. The adhesion layer also generally provides resistanceto oxide and carbide formation during CNT synthesis at elevatedtemperatures.

The interface layer is preferably formed from a metal which is oxidizedunder conditions of nanotube synthesis or during exposure to air afternanotube synthesis to form a suitable metal oxide. Examples of suitablematerials include aluminum. Alternatively, the interface layer may beformed from a metal oxide, such as aluminum oxide or silicon oxide.Generally, the interface layer is thin enough to allow the catalyticlayer and the adhesion layer to diffuse across it. In some embodimentswherein the catalytic layer and the adhesion layer have the samecomposition, this reduces migration of the catalyst into the interfacelayer, improving the lifetime of the catalyst during nanotube growth.

The catalytic layer is typically a thin film formed from a transitionmetal that can catalyze the formation of carbon nanotubes via chemicalvapor deposition. Examples of suitable materials that can be used toform the catalytic layer include iron, nickel, cobalt, rhodium,palladium, and combinations thereof. In some embodiments, the catalyticlayer is formed of iron. The catalytic layer is of appropriate thicknessto form catalytic nanoparticles or aggregates under the annealingconditions used during nanotube formation.

In other embodiments, the multilayer substrate serves as catalyticsurface for the growth of a CNT array. In these instances, the processof CNT growth using chemical vapor deposition alters the morphology ofthe multilayer substrate. Specifically, upon heating, the interfacelayer is converted to a metal oxide, and forms a layer or partial layerof metal oxide nanoparticles or aggregates deposited on the adhesionlayer. The catalytic layer similarly forms a series of catalyticnanoparticles or aggregates deposited on the metal oxide nanoparticlesor aggregates. During CNT growth, CNTs form from the catalyticnanoparticles or aggregates. The resulting CNT arrays contain CNTsanchored to an inert support via an adhesion layer, metal oxidenanoparticles or aggregates, and/or catalytic nanoparticles oraggregates.

In particular embodiments, the multilayer substrate is formed from aniron adhesion layer of about 30 nm in thickness, an aluminum or aluminainterface layer of about 10 nm in thickness, and an iron catalytic layerof about 3 nm in thickness deposited on a metal surface. In thisembodiment, the iron adhesion layer adheres to both the metal surfaceand the Al (alumina nanoparticles or aggregates after growth) or Al₂O₃interface layer. The iron catalytic layer forms iron nanoparticles oraggregates from which CNTs grow. These iron nanoparticles or aggregatesare also bound to the alumina below.

As a result, well bonded interfaces exist on both sides of the oxideinterface materials. Of metal/metal oxide interfaces, the iron-aluminainterface is known to be one of the strongest in terms of bonding andchemical interaction. Further, metals (e.g., the iron adhesion layer andthe metal surface) tend to bond well to each other because of strongelectronic coupling. As a consequence, the CNTs are strongly anchored tothe metal surface.

Further, subsurface diffusion of iron from the catalytic layer duringnanotube growth is reduced because the same metal is on both sides ofthe oxide support, which balances the concentration gradients that wouldnormally drive diffusion. Therefore, catalyst is not depleted duringgrowth, improving the growth rate, density, and yield of nanotubes inthe array.

In some embodiments, the CNT array is formed by vertically aligning aplurality of CNTs on the multilayer substrate described above. This canbe accomplished, for example, by transferring an array of CNTs to thedistal ends of CNTs grown on the multilayer substrate. In someembodiments, tall CNT arrays are transferred to the distal ends of veryshort CNTs on the multilayer substrate. This technique improves the bondstrength by increasing the surface area for bonding.

The inert support for the CNT array or sheet can be a piece of metalfoil, such as aluminum foil. In these cases, CNTs are anchored to asurface of the metal foil via an adhesion layer, metal oxidenanoparticles or aggregates, and catalytic nanoparticles or aggregates.In some instances only one surface (i.e., side) of the metal foilcontains an array or sheet of aligned CNTs anchored to the surface. Inother cases, both surfaces (i.e., sides) of the metal foil contain anarray or sheet of aligned CNTs anchored to the surface. In otherembodiments, the inert support for the CNT array or sheet is a surfaceof a conventional metal heat sink or heat spreader. In these cases, CNTsare anchored to a surface of the heat sink or heat spreader via anadhesion layer, metal oxide nanoparticles or aggregates, and catalyticnanoparticles or aggregates. This functionalized heat sink or heatspreader may then be abutted or adhered to a heat source, such as anintegrated circuit package.

B. Carbon Nanotube Sheets

Carbon nanotube sheets can be prepared using techniques well known inthe art. In one embodiment, the sheets are prepared as described in U.S.7,993,620 B2. In this embodiment, CNT agglomerates are collected intosheets in-situ inside the growth chamber on metal foil substrates. Thesheets can then be densified by removing the solvent. In anotherembodiment, the CNT sheets are made by vacuum filtration of CNTagglomerates that are dispersed in a solvent.

C. Coated Nanotube Arrays and Sheets

1. Polymer Coatings

Polymers to be coated can be dissolved in one or more solvents and sprayor dip coated or chemically or electrochemically deposited onto thevertical CNT forests or arrays grown on a substrate, or on a sheet, asdescribed above. The coating materials can also be spray coated inpowder form onto the top of vertical CNT forests or arrays grown on asubstrate, or on CNT sheets as described above. The coatings includespolymers or molecules that bond to CNTs through van der Waals bonds, π-πstacking, mechanical wrapping and/or covalent bonds and bond to metal,metal oxide, or semiconductor material surfaces through van der Waalsbonds, π-π stacking, and/or covalent bonds.

For spray or dip coating, coating solutions can be prepared bysonicating or stirring the coating materials for a suitable amount oftime in an appropriate solvent. The solvent is typically an organicsolvent or solvent and should be a solvent that is easily removed, forexample by evaporation at room temperature or elevated temperature.Suitable solvents include, but are not limited to, chloroform, xylenes,hexanes, pyridine, tetrahydrofuran, ethyl acetate, and combinationsthereof. The polymer can also be spray coated in dry form using powderswith micron scale particle sizes, i.e., particles with diameters lessthan about 100, 50, 40, 20, 10 micrometers. In this embodiment, thepolymer powder would need to be soaked with solvent or heated into aliquid melt to spread the powder particles into a more continuouscoating after they are spray deposited.

The thickness of the coatings is generally between 1 and 1000 nm,preferably between 1 and 500 nm, more preferably between 1 and 100 nm,most preferably between 1 and 50 nm. In some embodiments, the coatingthickness is less than 500, 450, 400, 350, 300, 250, 200, 150, 100, 90,80, 70, 60, 50, 40, 30, 20 or 10 nm.

Spray coating process restricts the deposition of coating to the CNTtips and limits clumping due to capillary forces associated with thedrying of the solvent. The amount of coating visible on the CNT arraysincreases with the number of sprays. Alternative techniques can be usedto spray coat the coating materials onto the CNT arrays includingtechniques more suitable for coating on a commercial scale.

In another embodiment that demonstrates a coating process, CNT sheetsare dipped into coating solutions or melted coatings to coat CNTsthroughout the thickness of the sheets, increasing the thermalconductivity of the sheet in the cross-plane direction by greater than20, 30, 50, or 70%. These coated sheets are then placed between a chipand heat sink or heat spreader with the application of solvent or heatto reflow the polymer and bond the CNT sheet between the chip and heatsink or spreader to reduce the thermal resistance between the chip andheat sink or heat spreader.

In other embodiments, the coating material can be deposited on the CNTarray or sheet using deposition techniques known in the art, such aschemical deposition (e.g., chemical vapor deposition (CVD)), aerosolspray deposition, and electrochemical deposition.

In one embodiment, a polymer coating can be applied by electrochemicaldeposition. In electrochemical deposition, the monomer of the polymer isdissolved in electrolyte and the CNT array or sheet is used as theworking electrode, which is opposite the counter electrode. A potentialis applied between the working and counter electrode with respect to athird reference electrode. The monomer is electrooxidized on the CNTarray tips or sheet sidewalls that face the electrolyte as a result ofthe applied potential. Controlling the total time in which the potentialis applied controls the thickness of the deposited polymer layer.

In some embodiments, the coating material is, or contains, one or moreoligomeric and/or polymeric materials. In particular embodiments, thepolymer can be a conjugated polymer, including aromatic and non-aromaticconjugated polymers. Suitable classes of conjugated polymers includepolyaromatic and polyheteroaromatics including, but not limited to,polythiophenes (including alkyl-substituted polythiophenes),polystyrenes, polypyrroles, polyacetylenes, polyanilines, polyfluorenes,polyphenylenes, polypyrenes, polyazulenes, polynaphthalenes,polycarbazoles, polyindoles, polyazepines,poly(3,4-ethylenedioxythiophenes), poly(p-phenyl sulfides), andpoly(p-phenylene vinylene). Suitable non-aromatic polymers include, butare not limited to, polyacetylenes and polydiacetylenes. The polymerclasses listed above include substituted polymers, wherein the polymerbackbone is substituted with one or more functional groups, such asalkyl groups. In some embodiments, the polymer is polystyrene (PS). Inother embodiments, the polymer is poly(3-hexythiophene) (P3HT).

In other embodiments, the polymer is a non-conjugated polymer. Suitablenon-conjugated include, but are not limited to, polyvinyl alcohols(PVA), poly(methyl methacrylates) (PMMA), polysiloxanes, polyurethanes,polydimethylsiloxanes (PDMS), and combinations (blends) thereof.

In other embodiments, the polymer is a paraffin wax. In otherembodiments, the polymer is a synthetic wax such as Fischer-Tropschwaxes or polyethylene waxes. In other embodiments, the polymer is a waxthat has a melting temperature above 80, 90, 100, 110, and 120° C.,preferably above 130° C.

In some other embodiments, the polymer is an adhesive, such as, but notlimited to, a hot glue or hot melt adhesive that combines wax,tackifiers and a polymer base to provide improved surface adhesion. Insome embodiments, the adhesive is a pressure sensitive adhesive. Incertain other embodiments the adhesive is a monomer that polymerizesupon contact with air or water such as a cyanoacrylate. In yet otherembodiments, the adhesive is a combination of a pressure sensitiveadhesive polymer and a thermally activated (or activatable) adhesivepolymer which enhances ease of adhesion of a multilayered or multitieredstructure described herein which includes such a combination of coatingsto a surface(s), by way of the pressure sensitive adhesive andadditional and more permanent or semi-permanent adhesion by way of thethermal adhesive.

2. Metallic Nanoparticles

The CNT arrays or sheets can be coated with one or more metalnanoparticles. One or more metal nanoparticles may be adsorbed to thedistal ends and/or sidewalls of the CNTs to bond the distal ends of theCNTs to a surface, reduce thermal resistance between the CNT array orsheet and a surface, or combinations thereof. Metal nanoparticles can beapplied to CNT arrays or sheets using a variety of methods known in theart. For example, a solution of metal thiolate such as palladiumhexadecanethiolate can be sprayed or spin coated onto the distal endsand/or sidewalls of the CNTs, and the organics can be baked off to leavepalladium nanoparticles. In another example, electron-beam or sputterdeposition can be used to coat metal nanoparticles or connected“film-like” assemblies of nanoparticles onto the distal ends and/orsidewalls of the CNTs. The metallic particles can be coatedsimultaneously with the coating or before or after coating.

Examples of suitable metal nanoparticles include palladium, gold,silver, titanium, iron, nickel, copper, and combinations thereof.

3. Flowable or Phase Change Materials

In certain embodiments, flowable or phase change materials can beapplied to the CNT array or sheet. Flowable or phase change materialsmay be added to the CNT array or sheet to displace the air between CNTsand improve contact between the distal ends of CNTs and a surface, andas a result reduce thermal resistance of the array or sheet and thecontact between the array or sheet and a surface, or combinationsthereof. Flowable or phase change materials can be applied to CNT arraysor sheets using a variety of methods known in the art. For example,flowable or phase change materials in their liquid state can be wickedinto a CNT array or sheet by placing the array or sheet in partial orfull contact with the liquid.

Examples of suitable flowable or phase change materials include paraffinwaxes, polyethylene waxes, hydrocarbon-based waxes in general, andblends thereof. Other examples of suitable flowable or phase changematerials that are neither wax nor polymeric include liquid metals,oils, organic-inorganic and inorganic-inorganic eutectics, and blendsthereof. In some embodiments, the coating material(s) and the flowableor phase change material are the same.

The coatings, metallic particles, and/or flow or phase change materialsdescribed above can be applied directly to the CNT arrays or sheets andthe coated CNT arrays or sheets can subsequently be stacked to formmultilayered or multitiered structures. In certain other embodiments,the coatings, metallic particles, and/or flow or phase change materialsdescribed above are applied during the stacking of two or more CNTarrays or sheets. In still other embodiments, the coatings, metallicparticles, and/or flow or phase change materials described above areapplied following the stacking of two or more CNT arrays or sheets. Innon-limiting embodiments, multilayered or multitiered structure(s) areformed by first stacking two or more CNT arrays or sheets and then theat least partially interdigitated tiers of the formed structures areinfiltrated with one or more coatings, metallic particles, and/or flowor phase change materials, or combinations thereof. The introduction ofsuch coatings/materials into the at least partially interdigitated tiersof the multilayered or multitiered structure(s) prior to, during, orafter stacking can be used to modify and/or enhance the thermaltransport or thermal resistance properties of the multilayered ormultitiered structures resulting from the stacking of the CNT arrays orsheets.

D. Multilayered or Multitiered Structures

In the embodiments described herein, the multilayered or multitieredstructures formed by stacking of CNT arrays or sheets are formed by amethod including the steps of:

(1) providing at least two or more CNT arrays or sheets; and

(2) stacking the at least CNT arrays or sheets

wherein the stacking results in at least partial interdigitation of thenanostructures, CNTs, of the arrays or sheets. In some embodiments, themethod of making the multilayered or multitiered structures furtherincludes a step of applying or infiltrating a coating, a coating ofmetallic nanoparticles, and/or a coating of flowable or phase changematerials, which are described above. In some embodiments, the step ofapplying or infiltrating a coating, a coating of metallic nanoparticles,and/or a coating of flowable or phase change materials occurs prior tostacking, alternatively during stacking, or alternatively afterstacking. In yet other embodiments, the method includes applyingpressure during the stacking step. The applied pressure may be in therange of about 1-100 psi, 1-50 psi, 1-30 psi, more preferably about 1-20psi, and most preferably about 1-15 psi. In some embodiments, thepressure is about 15 psi. Pressure may be applied continuously until theadjacent tiers are bonded, if a coating material(s) which can act as abonding agent, such as an adhesive or phase change material, is used.Pressure may be applied for any suitable amount of time. In someembodiments, only a short time is used, such as less than 1 minute, ifno bonding agent is used.

At least two CNT arrays or sheets can be stacked to form themultilayered or multitiered structures. For example, FIG. 2 showsstacking of three CNT arrays (right side). By using more CNT arrays thethickness of the multilayered or multitiered structures can be increasedas needed. In some embodiments, up to 5, 10, 15, 20, 25, 30, or more CNTarrays or sheets can be stacked according to the method described above.The thickness of the resulting multilayered or multitiered structuresformed by stacking can be in the range 1-10,000 microns or more.

In certain embodiments, the multilayered or multitiered structures canbe formed by stacking multiple tiers of CNT arrays in a stepped manner,off-set manner, and/or other non-uniform manner in order to be able toconform to complex surfaces.

In a non-limiting embodiment, at least two vertically aligned arrays orsheets formed on supports/substrates are stacked/contacted such that thenanostructure elements, such as CNTs, of the arrays at least partiallyinterdigitate on contact. In one embodiment full interdigitation ofnanostructure elements of the arrays occurs within one another whenstacked. In other embodiments the arrays may interdigitate only at thetips of the nanostructure elements, such as CNTs. In yet otherembodiments, the individual nanostructures can navigate through thenanostructures of the adjacent array during the interdigitating process.

In some embodiments the nanostructures of the stacked arrays, whichinterdigitate at least partially, may also form into largersuperstructures, such as, but not limited to, tube bundles, clumps, orrows. These superstructures may be formed through mechanisms such ascapillary clumping or by way of application of a polymer coating priorto, during, or following the stacking process.

In some embodiments, a polymer coating and/or adhesive, or other coatingas described above, is applied to the CNT array(s) which are thenstacked. In such embodiments, the thickness of the coating and/oradhesive, or other coating as described above, is about 1-1000 nm, morepreferable 1-500 nm, and most preferably 1-100 nm.

In certain embodiments of the above method, following the stacking stepthe method further includes a step of applying an adhesive, such as butnot limited to a hot glue or hot melt adhesive that combines wax,tackifiers and a polymer base to the resulting stack to provide improvedadhesion properties to one or more surfaces of the stacked/tiered CNTarrays forming the multilayered or multitiered structure. In someembodiments, the adhesive is a pressure sensitive adhesive. In yet otherembodiments, the adhesive is a combination of a pressure sensitiveadhesive polymer and a thermally activated (or activatable) adhesivepolymer which enhances ease of adhesion of a multilayered or multitieredstructure described herein which includes such a combination of coatingsto a surface(s), by way of the pressure sensitive adhesive andadditional and more permanent or semi-permanent adhesion by way of thethermal adhesive.

In yet other embodiments, one or more tiers of the stacked arraysdescribed above may be substituted with other materials to afford acomposite stack. Such materials include, but are not limited to,solders, greases, adhesives, phase change materials, gels, heatspreaders, compliant pads, and/or (elastomeric) gap pads. Thesubstitution of these materials for one or more CNT array tiers of themultiered or multilayered stacks described can be used to further tunethe properties of the resulting composite stack. Such composite stacksmay be used for a variety of applications described below, such asthermal interface materials (TIMs).

Yet another option is introduce a dielectric material or induce theformation of a dielectric material within the layers/tiers of stackedarrays in order to convert the resulting composite stack from anelectrical conductor into an insulator. Dielectric materials are knownin the art, such as ceramic insulating materials. As one example, one ormore of the substrates of the CNT arrays present in a multitiered stack,which is formed from aluminum, can oxidized (such as by anodization) toproduce an electrically insulating stack.

V. Applications

The multilayered or multitiered structures formed by stacking of CNTarrays or sheets described herein can be used as thermal interfacematerials (TIMs). The multilayered or multitiered structures formed bystacking of CNT arrays or sheets can be formed and/or deposited, asrequired for a particular application.

Accordingly, such materials are well suited for applications whererepeated cycling is required. For example, they can be employed asthermal interface materials (TIMs) during ‘burn-in’ testing ofelectrical components, such as chips or circuits. In some embodiments,the inert support/substrate is a surface of a conventional metal heatsink or spreader. This functionalized heat sink or spreader may then beabutted or adhered to a heat source, such as an integrated circuitpackage. Such TIM materials can also be placed or affixed in between aheat source and a heat sink or heat spreader, such as between anintegrated circuit package and a finned heat exchanger, to improve thetransfer of heat from the heat source to the heat sink or spreader.

The high elastic recovery of the multilayered or multitiered structuresformed by stacking of CNT arrays or sheets described when furthercontaining an adhesive coating advantageously allows the TIMs formedthereof to maintain intimate contact between surfaces as the surfacesbow or otherwise deform due to thermal expansion. Multilayered ormultitiered TIM structures having an adhesive coating can have adhesionstrengths of at least about 1000, 750, 500, 450, 400, 350, 300, 250,200, 150, or 100 psi. The presence of one or more adhesives forming partof the TIMs described generally result in no thermal penalty (i.e., nonotable decrease in thermal performance properties) for the TIM, ascompared to a TIM lacking the presence of adhesive(s).

The TIM structures formed from the multilayered or multitieredstructures formed by stacking of CNT arrays or sheets described hereinmay also be applied to node multi-chip modules (MCMs). In particular,the TIM structures may be adjusted to have 2, 3, 4, or more tiers inorder to allow for uniform or essentially uniform contact with MCMs. Incertain instances it can be difficult to predict or model warpage whichmay occur in individual chips, circuits, or MCMs during operation atnormal temperatures. Warpage can lead to defects and even to failure incertain instances. Accordingly, TIM structures described areparticularly suitable for such applications because they can be readilyadjusted, if needed, to meet the tolerances required for suchapplications. As a microchips heat up, they can warp leading to a centerto-edge warpage greater than 50 μm whereas in multichip applications,the TIMs described here can accommodate chip-to-chip offsets of 100 μmor more and/or can also accommodate chip center-to-edge warpages ofgreater than 50 μm.

The CNT arrays and the multilayered or multitiered structures formed bystacking of such CNT arrays described herein can be used as thermalinterface materials (TIMs) in personal computers, server computers,memory modules, graphics chips, radar and radio-frequency (RF) devices,disc drives, displays, including light-emitting diode (LED) displays,lighting systems, automotive control units, power-electronics, solarcells, batteries, communications equipment, such as cellular phones,thermoelectric generators, and imaging equipment, including MRIs. TheCNT arrays and the multilayered or multitiered structures formed bystacking of such CNT arrays can also be used as efficient heat spreaderswhen a sufficient number of tiers (i.e., 2, 3, 4, 5, or more tiers) arepresent such that the substrate that the CNTs are grown on provide anin-plane thermal conductivity which is on par with that of the basematerial of the substrate, which is typically a metal. In certainembodiments, the multilayered or multitiered structures can be formed bystacking multiple tiers of CNT arrays in a stepped manner, off-setmanner, and/or other non-uniform manner in order to more readily conformto complex surfaces, such as those of MCMs, which are typicallynon-uniform. In such instances, customized multilayered or multitieredstructures may be designed and formed by stacking two or more CNT arraytiers in a manner that conforms to the complex surface of a givendevice.

In certain embodiments, the multilayered or multitiered structuresformed by stacking of CNT arrays are useful in low contact pressureand/or low pressure applications. Low pressure may refer to ambientpressure or pressures below 1 atm, such as in the range of about 0.01 toless than about 1 atm. In some instances, low pressure may refer to avacuum such as in aerospace applications where such TIMs could be usedin satellites or space vehicles/systems.

In certain embodiments, the multilayered or multitiered structuresformed by stacking of CNT arrays are useful at temperatures which arebelow ambient temperature, below freezing, or at cryogenic temperatures(such as experienced in space).

The CNT arrays and the multilayered or multitiered structures formed bystacking of such CNT arrays described herein can also be used forapplications other than heat transfer. Examples include, but are notlimited to, microelectronics, through-wafer vertical interconnectassemblies, and electrodes for batteries and capacitors. Currently,copper and aluminum foil are used as the backing materials for the anodeand cathode in lithium ion batteries.

The multilayered or multitiered structures formed by stacking of suchCNT arrays could also be used for electromagnetic shielding.

EXAMPLES Example 1. Multilayered/Multitiered CNT-Based Thermal InterfaceMaterials (TIMs)

Methods:

Thermal Measurement System Design

Heat transfer properties for all test specimens were evaluated using atest fixture (not shown) designed and built based on the methodsdescribed in ASTM D5470 “Standard Test Method for Thermal TransmissionProperties of Thermally Conductive Electrical Insulation Materials.” Itnot only allows for deformation of the test specimens but alsoincorporates a vacuum chamber to minimize conductive and convective heatlosses. The vacuum chamber was constructed of stainless steel with anacrylic door, and is capable of maintaining vacuum in the 10⁻⁵ torrrange. The vacuum chamber sits on the reaction plate of a 1000 lb loadframe, with all feedthroughs near the top of the chamber. Thermocoupleswere fed via a pair of Omega 4-pair feedthroughs (8 thermocouplespossible). The cooling tubes possess bulkhead fittings with o-ringseals. The power for the heaters were controlled via a Watlow SDcontroller with a thermocouple feedback loop. The heating block wassurrounded by an FR 4 fiberglass insulator shell and the cooling blocksits atop a fiberglass insulative plate with machined recessed sectionsto maintain centrality with the heating block. Both 1″×1″ and 4″×4″heating blocks and cooling blocks were fabricated to accommodate plannedtesting for this program.

Heat Transfer Coefficient Evaluation

Heat transfer evaluations were conducted with a 20° C. differentialbetween the hot and cold meter blocks of the test fixture. It was foundthat a temperature differential as close as possible to 20° C. wasrequired to drive heat transfer in the system such that accurate resultscould be obtained. Test data were imported directly from the data outputfile of the test, which was acquired via LabView. The ThermalConductivity (λ) of the meter bars (5005 series Aluminum) was calculatedfor the specific temperature using the algorithm for aluminum from NIST(E. Marquardt, J. Le, and R. Radebaugh, “Cryogenic Material PropertiesDatabase Cryogenic Material Properties Database,” 2000).

Heat flow through each individual meter bar was then calculated fromEquation 1:Q=(λ*A/d)(δT)  (1)where Q is the heat flow through the bar, A is cross sectional area, dis the distance between thermocouples and δT is the difference intemperature from one thermocouple to the other in Kelvin. The values forthe hot and cold meter blocks were then averaged to gain Q_(TOTAL).Thermal impedance in m² K/W was then evaluated through Equation 2:θ=(A/Q _(AVG))*δT  (2)where δT=T_(H)−T_(C) is the difference between the specific temperaturesat the interface of the evaluated material and the meter blocks, A isthe cross sectional area of the material, and Q is the average heat flowthrough the meter blocks.

Thermal conductivity was then calculated using Equation 3:λ=Q _(AVG) *δd/A*δT  (3)where δd is the change in thickness of the specimen, A is crosssectional area of the specimen and δT is the temperature differenceacross the specimen in Kelvin.

The heat transfer coefficient of the test specimens was calculated viaEquation 4:c=Q _(AVG) /A*δT  (4)

Sample Fabrication:

CNT arrays were grown on both aluminum (Al) and copper (Cu) substratesusing an iron catalyst to evaluate their differences in performance. CNTgrowth was performed using a low-pressure chemical vapor deposition(LPCVD) process.

Three different CNT height-foil combinations were tested:

-   -   Series #1-50 micron Al substrate with 50 micron nanotubes on        each side    -   Series #2-50 micron Al substrate with 75 micron nanotubes on        each side    -   Series #3-50 micron copper substrate with 150 micron nanotubes        on each side

In general, the nanotube quality was very good for all lengthsfabricated. However as the tube length increased, the presence ofdefects also increased. Furthermore, the ultimate achievable height ofthe CNTs was limited by back diffusion of the catalyst into thesubstrate and diffusion of the substrate into the catalyst stack. Forapplications where thicker samples with more compliance were required,an increased height of the TIM was achieved by stacking double-sidedforests/arrays. As shown schematically in FIGS. 1A and 1B, a thermalinterface material (TIM) having a single tier, 100, with arrays ofcarbon nanotubes, 110, on each side of the substrate and wherein the TIMcan be placed between an electronic device, 200, and a heat sink, 300(FIG. 1A) and a thermal interface material (TIM) having, for example,three tiers, 100, can be placed between an electronic device, 200, and aheat sink, 300.

Two different stack configurations utilizing single TIMs on aluminum(Al) substrates were evaluated. The first configuration, denoted “dry”stack, was assembled from three individual TIMs and then evaluated asprepared. The second stack configuration involved bonding the individualTIMs together at the tube-to-tube interfaces using a very thin sprayedon wax material. These sprayed-on interface materials have been shown todramatically decrease thermal resistance in CNT-based thermal interfacematerials. The maximum usable temperature for the synthetic wax is 150°C., well within the expected operating range of these TIMs and the verythin layers (˜100 nm) employed are not expected to present anyoutgassing issues.

All initial evaluations were conducted at ambient pressure with anaverage temperature of 50° C. and a temperature differential of 20° C.between the heated and cooled meter blocks in the test fixture. Once thethermal performance of the first and second configuration TIM stacks hadbeen verified at ambient pressure, additional testing was conductedunder vacuum. A median temperature of 50° C. and a temperaturedifferential of 20° C. were used to enable comparison with ambientpressure data.

Results and Discussion:

Dry Stacks

Actual displacements measured with the instrument crosshead ranged from430 μm to 480 μm with an applied pressure of 10 kPa (1.5 psi) and from355 μm to 460 μm with an applied pressure of 69 kPa (10 psi). Thissuggested some combination of CNT buckling and/or interfaceinterdigitation. It is noted that the displacement measurement is notthe same as a true thickness in that it can be difficult to discernexactly the point at which contact to the TIM stack is made for thedisplacement measurement. CNT buckling and interdigitation of adjacentCNT layers must also be considered. However, exact thicknessmeasurements are not possible using conventional measuring techniques.

Results of heat transfer testing for two dry TIM stacks are shown inFIG. 2. Each specimen was tested through the entire 10-69 kPa (1.5 to 10psi) pressure cycle twice to assess reproducibility of the dry stacks.For both of the dry stacks tested, there was a substantial improvementin heat transfer after having experienced one pressure cycle. Thissuggested that an assembly pressure was required in order to ensure goodcontact between adjacent CNT layers. This demonstrates the improvementin heat transfer resulting from interdigitation.

Wax-Assembled Stacks

In these experiments, three TIM specimens on aluminum substrates, eachwith a total thickness of approximately 200 μm, were stacked and bondedwith a thin wax layer (˜100 nm) to provide a TIM assembly of roughly 600μm (0.024″) in thickness. Actual displacements measured with theinstrument crosshead were somewhat less than the target thickness.

Test results for the wax-bonded stacks are provided in FIG. 3. Ingeneral, the wax stacks are more consistent in performance than the drystacks and do not appear to require a “break-in” pressure cycle beforeperforming well. A performance anomaly was noted for specimen B2 at lowcontact pressure in Test 1; this might be due to insufficient contactbetween the upper meter block and the specimen in the fixture.Subsequent tests of this particular specimen consistently showedexcellent performance. Stacking TIMs, as described herein, allowsgrowing long CNTs on metal substrates, especially when a thin (˜nmthick) layer of polymer is used to bond the inter-tier layers andcontrol the level of interdigitation.

Example 2: Multilayered/Multitiered CNT-Based Thermal InterfaceMaterials (TIMs) Containing Polymer or Adhesive

CNT arrays were grown to nominally 100 μm thickness and fullyinfiltrated with a soft polyurethane polymer. The thermal resistance ofeach individual pad was measured using a modified ASTM D570 stepped barapparatus.

The individual samples were stacked using various methods, and thethermal resistance of the resulting stack was measured in the samemanner as the single tiers.

First, two individual array samples with measured thermal resistances of1.37 and 1.5 cm²-K/W respectively were stacked on top of one another.Solvent known to dissolve the polymer that was used to infiltrate thearray was placed between the stacks to place the interface in a liquidstate. The resulting stack was allowed to dry under pressure until thesolvent was fully evaporated. The stack was then measured in the steppedbar system with a resulting resistance of 1.5 cm²-K/W. In this example,the thickness of the stacked array was doubled while incurring nopenalty in thermal resistance.

In a second experiment, two individual array samples with thermalresistances of 0.45 and 0.66 cm²-K/W respectively were stacked on top ofone another. A thin layer of acrylate adhesive was placed between thesamples. The sample stack was allowed to dry under pressure until thesolvent was fully evaporated. The resulting stack was then measured inthe stepped bar system with a resulting resistance of 0.66 cm²-K/W. Inthis second example, the thickness of the stacked array was also doubledwhile incurring no penalty in thermal resistance.

Example 3. Multilayered/Multitiered CNT-Based Thermal InterfaceMaterials (TIMs)

Sample Fabrication:

Vertically aligned carbon nanotube (CNT) arrays were grown on aluminumfoil as the base substrate. Both sides of 50 μm thick aluminum foil werecoated with an iron catalyst layer and the CNTs were grown via lowpressure chemical vapor deposition with acetylene and hydrogen asprecursor gases and growth being performed at 630° C. in order to staybelow the melting temperature of the Al substrate. CNTs were grown to7-10 μm on both sides of the substrate with an 8 minute growth time.One-tier CNT-based thermal interface material (non-stacked) and two- andfour-tiered (formed by stacking two or four double-sided CNT arrays)CNT-based thermal interface materials (TIMs) having an area of 1 cm×1 cmwere prepared for testing.

Testing Methods:

In order to measure the thickness, compression, and rebound of the oneand three-tiered TIMs prepared, a Precision Thickness Gauge-FT3V byHanatek® Instruments having a weight platform and a pressure foot (notshown) was used to measure the thickness at different applied pressures.Weights can be added to a weight platform of the instrument thatcorresponds to an instantaneous change in pressure at the pressure footof the instrument that the TIM material being tested is placed under.The pressure foot comes down at a rate of 3 mm/s. The thickness wasrecorded when the TIM material being tested had reached a steady state,which typically took about 1-10 seconds. For a given user applied force,the instrument measured the thickness with an accuracy of +/−0.1micrometer. The instrument met ASTM-F36-99 standards to testcompressibility and recovery of gasket materials. The minimum pressurethe gauge of the instrument was able to achieve is 7 psi—the datumpressure. The pressure was then taken up to 100 psi and the thicknesswas recorded. Then, all pressure was released from the TIM materialbeing tested, and then the 7 psi was re-applied to measure the amount ofrebound of the TIM material being tested.

To benchmark the thermal performance of the TIMs, as a function ofnumber of tiers (i.e., one-, two-, and four-tiered CNT-based TIMs), thesamples were measured in a modified ASTM-D5470 stepped bar apparatusdesigned to measure the steady state 1 D thermal resistance of thermallyconductive samples. The ASTM-D5470 stepped bar test apparatus isdescribed in detail in D. R. Thompson, S. R. Rao, and B. A. Cola, “Astepped-bar apparatus for thermal resistance measurements,” Journal ofElectronic Packaging, vol. 135, p. 041002, 2013.

The performances of the single and three-tiered CNT-based TIMs werecompared to TIMs known in the art. Accordingly a variety of commerciallyavailable TIMs were also tested under the same conditions. Thecommercial TIMs used for benchmarking were: TGARD® 210 (siliconeelastomer), TGlobal PC94® (acrylic base), Pyrolytic Graphite (PGS),Fujipoly® SARCON XR-UM-Al (a silicone putty backed with a thin aluminumfoil), and Indium Heat Spring (a soft metal). These materials werechosen to represent different TIM compositions, and all possessed aspecified thermal conductivity of greater than 4.0 (W/m-K), which isconsidered state of the art for currently available TIMs.

Compressibility of the tested TIMs was determined according to Formula(5) below:(thickness_(100psi)/thickness_(original))  (5)TIM rebound, wherein in “rebound” as used herein refers to the degree towhich a TIM recovers to its original thickness, was determined accordingto Formula (6) below:

$\begin{matrix}\left( \frac{{thickness}_{{post}\mspace{14mu}{compression}} - {thickness}_{100\mspace{14mu}{psi}}}{{thickness}_{original} - {thickness}_{100\mspace{14mu}{psi}}} \right) & (6)\end{matrix}$

Results:

FIG. 4 and FIG. 5 show the normalized compression and rebound,respectively of the one-, two-, and four-tiered CNT-based TIMs, as wellas the benchmarking commercial TIMs. When looking at commercial TIMs, asshown in FIG. 4, most demonstrated a compressibility of 10% or less, at100 psi. Stacked two and four-tiered CNT-based TIMs showed a slight dropin compressibility, as compared to a single tiered CNT-based TIM, whichis believed to result from inter-digitation of the CNT tips during thestacking process. Indium and the PC94 TIMs had notably highercompressibility at 100 psi at 33% and 16%, respectively. However, thesematerials have comparatively little rebound after the initialcompression. In applications with cyclic heating and cooling, this couldlead to undesirable dewetting of the interface during expansion andcontraction events.

From a deformation mechanics perspective, the CNT-based TIMS andpyrolytic graphite (PGS) have a good combination of compressibility andrebound after compression. However, a key challenge in the selection ofa TIM for applications requiring compliance is that the warpage of achip or die in the application is not always known. As a means ofevaluating the required compliance of an application, one may considerstacking CNT-based TIMs in the interface. Because the CNT-based TIMs donot experience an inter-tier thermal penalty, the effective thermalconductance of the stack increases with each successive tier due tocompliance driven increased contact area for applications with a curvedinterface. Such an effect was shown for CNT-based TIMs having one-,two-, and four-tiers which were successfully compressed on a curvedinterface (not shown) and which demonstrated that the resulting contactarea was clearly increased with each additional tier present. At fourtiers, contact appeared to be approximately uniform across theinterface.

When measured in the stepped bar apparatus, the relative thermalconductance of the one-, two-, and four-tiered CNT-TIMs was found toincrease by 95% when going from one to two tiers, and an additional 36%when going from two to four tiers (see FIG. 6). Thermal conductivity orconductance can be determined using Eqn. (3) whereas relative thermalconductance is determined according to formula (7) below:

$\begin{matrix}\left\lbrack \frac{conductance}{{conductance}_{{single}\mspace{14mu}{tier}}} \right\rbrack & (7)\end{matrix}$where conductance refers to the conductance of a multitiered TIM. As thebulk conductivity of the CNT-based TIMs did not increase with stacking,this effect was believed to be driven by the increase in contact areathat additional compliance allowed for.

In summary, bulk conductivity alone was not sufficient to predict how aTIM would perform at an interface. The compressibility of the TIM wasfound to be a key factor in evaluating the degree to which the TIM wouldbe able to create good contact at an interface with non-flat surfacesdue to warping or warpage, to meet manufacturing tolerances, 2.5 D or 3Darchitectures, or other scenarios found in varying applications.Furthermore, in applications that may heat and cool cyclically, or wherethe interface geometry may otherwise change on the microscale over time,TIM rebound required that the interface not de-wet which can result in aloss in performance during operation.

Example 4. Multilayered/Multitiered CNT-Based Thermal

Interface Materials (TIMs)

Sample Fabrication:

TIMs were prepared as described in Example 3 above.

Testing Methods:

Compliance and compression sets of a CNT-based stacked TIM is shown inFIG. 7, wherein the y-axis shows the change in thickness uponcompression to different pressures and recovery upon rest. Severalcycles were measured using a Precision Thickness Gauge-FT3V by Hanatek®Instrument, where “at rest” pressure measurements were taken at 7 psi,which is the minimum pressure achievable by the instrument. Dwell timeswere held for one minute at pressures of 30, 50, 60, or 80 psi. Thetotal time for each test cycle (i.e., at rest-high pressure dwelltime-at rest) was less than two minutes. Following each test cycle, theCNT-based stacked TIM was held at 0 psi (i.e., no contact with testinginstrument anvil) for a period of ten minutes in order to evaluate theTIM's slow elastic recovery component. All testing was performed at 80°C.

Thermal resistance of the CNT-based stacked TIM was measured with amodified ASTM D5470 stepped bar test apparatus (described above). Asshown in FIG. 8, the thermal resistance of the CNT-based stacked TIMdecreased from about 0.8 cm²-K/W to about 0.6 cm²-K/W upon increasingthe contact pressure up to 200 psi. Durability of the thermalperformance of the CNT-based stacked TIM was tested by repeated testcycling of the TIM at an interface pressure of 80 psi over greater than5,000 cycles. As shown in FIG. 9, thermal performance of the CNT-basedstacked TIM remained essentially constant over the greater than 5,000testing cycles showing the durability of the tested TIM. As shown inFIG. 10, thermal resistance hysteresis was found believed to be a resultof the superior mechanical properties of CNT-based stacked TIMs whichprovide for stable operation over a wide pressure range, up to at least500 psi, with easy rework.

FIG. 11 shows the performance of stacked CNT-based TIMs including (1) asingle-tiered CNT-based TIM, (2) a three-tiered CNT-based TIM, (3) aCNT-based TIM wherein a gap pad was sandwiched between two tiers ofCNT-based TIM, and (4) and an indium benchmarking sample. The thermalresistance when evaluated as a function of junction temperature and itwas shown that the stacked CNT-based TIM provided the lowest resistancewhen a device operates at its highest power due to die warpage, forexample. Under certain conditions, stacked CNT-based TIMs can provideadditional compliance and heat spreading for hot spots which may bepresent on a device, such as a chip, die, or MCM.

Lastly, FIG. 12 shows the effects of pressure on the normalizedthickness of different TIMs including: (1) an aluminum backed gap pad(of 230 μm thickness), (2) a carbon fiber filled gap pad (of 500 μmthickness), (3) a custom stacked CNT-based TIM with an integratedcompliant material, and (4) a custom stacked CNT-based TIM with anintegrated heat spreader. Custom stacked CNT-based TIMs which includeadditional integrated materials, such as heat spreaders, graphite,and/or gap pads, allow for further customization of the resulting TIMsfor use in particular applications having particular and/or uniquemechanical and/or performance requirements.

Unless defined otherwise, all technical and scientific terms used hereinhave the same meanings as commonly understood by one of skill in the artto which the disclosed invention belongs. Publications cited herein andthe materials for which they are cited are specifically incorporated byreference.

Those skilled in the art will recognize, or be able to ascertain usingno more than routine experimentation, many equivalents to the specificembodiments of the invention described herein. Such equivalents areintended to be encompassed by the following claims.

We claim:
 1. A method of forming a multilayered or multitiered structurecomprising the steps of: providing at least two planar substrates, eachindependently comprising vertically aligned carbon nanotubes grown fromopposing surfaces of the planar substrate; and stacking the at least twoplanar substrates; wherein the stacking results in at least partialinterdigitation between the vertically aligned carbon nanotubes of eachof the at least two planar substrates; and wherein the multilayered ormultitiered structure, when contacted with one or more surfaces of amaterial, conforms to asperities present on the one or more surfaces ofthe material.
 2. The method of claim 1, further comprising a step ofapplying a coating material or infiltrating a coating material onto thevertically aligned carbon nanotubes of the at least two planarsubstrates prior to, during, or after the stacking step.
 3. The methodof claim 1, further comprising applying pressure in the range of betweenabout 1 and 15 psi during the stacking step.
 4. The method of claim 1,wherein the at least two planar substrates are formed of metal.
 5. Themethod of claim 2, wherein at least some of the interstitial spacebetween the vertically aligned carbon nanotubes, surfaces of thevertically aligned carbon nanotubes, or both, of each of the at leasttwo planar substrates is infiltrated with the coating material, which issolidified within the vertically aligned carbon nanotubes of the arrays.6. The method of claim 2, wherein the coating material reduces theresistance to energy transport between the at least partiallyinterdigitated vertically aligned carbon nanotubes interfacing betweenthe stacked at least two planar substrates.
 7. The method of claim 2,wherein the vertically aligned carbon nanotubes interfacing between thestacked at least two planar substrates are chemically bonded by thecoating material which is an adhesive, a phase change material, or acombination thereof.
 8. The method of claim 7, wherein the adhesivecomprises a combination of a pressure sensitive adhesive and a thermallyactivatable adhesive.
 9. The method of claim 7, wherein the stacked atleast two planar substrates are bonded by reflowing the coating materialby applying heat or a solvent, followed by a step of drying.
 10. Themethod of claim 1, wherein the multilayered or multitiered structurecomprises three, four, or five layers of the planar substrates.
 11. Themethod of claim 1, wherein the multilayered or multitiered structure isa thermal interface material.
 12. The method of claim 1, wherein thethermal interface material has an adhesion strength of up to about 1,000psi.
 13. The method of claim 11, wherein the thermal interface materialfurther comprises including a layer or tier formed of a materialselected from the group consisting of a heat spreader, a compliant pad,and a gel present within the multilayered or multitiered structure. 14.The method of claim 11, wherein the thermal interface material furthercomprises including a dielectric layer present within the multilayeredor multitiered structure.
 15. The method of claim 1, further comprisingincluding a layer or tier formed of a material selected from the groupconsisting of a heat spreader, a compliant pad, and a gel which ispresent within the multilayered or multitiered structure.
 16. Amultilayered or multitiered structure formed by the method of claim 1.